Skip to main content

Real and Complex Measures

  • 41k Accesses

Part of the Graduate Texts in Mathematics book series (GTM,volume 282)


A measure is a countably additive function from a s-algebra to [0,α]. In this chapter, we consider countably additive functions from a s-algebra to either R or C. The first section of this chapter shows that these functions, called real measures or complex measures, form an interesting Banach space with an appropriate norm.

Author information

Authors and Affiliations


Rights and permissions

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (, which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Reprints and Permissions

Copyright information

© 2020 Sheldon Axler

About this chapter

Verify currency and authenticity via CrossMark

Cite this chapter

Axler, S. (2020). Real and Complex Measures. In: Measure, Integration & Real Analysis. Graduate Texts in Mathematics, vol 282. Springer, Cham.

Download citation